Resumen de Some Diophantine equations from finite group theory: \Phi_m(x) = 2 p^n - 1

Florian Luca, Pieter Moree, Benne de Weger

• We show that the equation in the title (with m the mth cyclotomic polynomial) has no integer solution with n  1 in the cases (m; p) = (15; 41), (15; 5581), (10; 271).

  These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami